8.10: Drive Away

Look at the fact and graph below. Can you figure out what Bush's speed was in miles per hour? Can you complete a table to show the total number of miles traveled by Bush at that speed? Can you write a rule to show how the number of miles is related to the number of hours? In this concept, we will learn how to interpret graphs and write rules to match what we see on graphs.

Fact: The graph shows the speeds of drivers, Axel and Bush, on city roads. Bush is traveling faster than Axel.

Guidance

In order to make a table and write a rule for situations like the one above, we can use the problem solving steps to help.

First,
describe
what you know. What information do we see in the graph?

Second, identify what
your job
is. In these problems, your job will be to make a table and write a rule.

Third, make a
plan
. In these problems, your plan should be to use the graph to fill in the table. Then, look for a pattern to help you write the rule.

Fourth,
solve
. Implement your plan.

Fifth,
check
. Make sure your rule works with the graph.

Example A

Fact: The graph shows the speeds of drivers, Harold and French. Harold didn’t travel as fast as French.

What was Harold’s speed in miles per hour?

Complete a table to show total number of miles traveled by Harold at that speed.

Let
represent number of hours and
represent distance in number of miles. Write a rule to show how the number of miles
is related to number of hours
.

Solution:

We can use problem solving steps to help us to interpret the graph and answer the questions.

Example B

Complete a table to show total number of miles traveled by Clark at that speed.

Let
represent number of hours and
represent distance in number of miles. Write a rule to show how the number of miles
is related to number of hours
.

Solution:

We can use problem solving steps to help us to interpret the graph and answer the questions.

Concept Problem Revisited

Fact: The graph shows the speeds of drivers, Axel and Bush, on city roads. Bush is traveling faster than Axel.

What was Bush’s speed in miles per hour?

Complete a table to show total number of miles traveled by Bush at that speed.

Let
represent number of hours and
represent distance in number of miles. Write a rule to show how the number of miles
is related to number of hours
.

We can use problem solving steps to help us to interpret the graph and answer the questions.

Vocabulary

A
graph
is one way to show the relationship between two variables. In this concept, we looked at graphs that showed the relationship between distance and time. A
table
is another way to show a relationship between two variables (often thought of as the
input
and the
output
). In this concept, the inputs of our tables were
number of hours
and the outputs of our tables were
number of miles.
A
rule
is an equation that can describe the relationship between the variables in a graph or a table. In this concept, we wrote
rules
that showed the relationship between the number of hours and the number of miles.